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In other words, the assumption that fg = fh allows us to link the geometric and probabilistic interpretations of the spectrum Points on a smooth contour have an such that: fh ( ) = 1 because a smooth contour lls the space as a line fg ( ) = 1 because a smooth contour has a given probability to appear In fact, we may de ne the point type (ie edge, corner, smooth region, etc) through its associated f ( ) value; a point x with f ( (x)) = 1 is called an edge point, a point x with f ( (x)) = 2 is called a smooth point, and, more generally, for t [0, 2], x is called a point of type t if f ( (x)) = t A bene t of the multifractal approach is thus that it allows us to de ne not only edge points, but a continuum of various types of points An important issue lies in the choice of a relevant sequence of capacities for describing the scene The problem of nding an optimal c in a general setting is unsolved In practice, we often use the following Assume the image is de ned n on [0, 1] [0, 1] Let P := ((Ik )0 k< n )1 n N be a sequence of partitions of n n n n [0, 1] [0, 1] and (xk , yk ) be any point in Ik Each Ik is made of an integer number n n of pixels Let L(Ik ) denote the sum of the gray levels in Ik Let (x, y) denote a generic pixel in the image and L(x, y) denote the gray level at (x, y) Let (pn )1 n N be a xed sequence of positive integers and be a region in the image sum measure: cs ( ) =.

(x,y)

.

L(x, y)

n+p L(Ik n )

cM ( ) = max L(x, y)

(x,y)

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In the rst approach each node is acting completely autonomously Cooperation is achieved by each node sharing with all (or a subset of) other nodes its intrusion detection data or alerts The second approach is the hierarchical approach in which the responsibilities of nodes are structured through a hierarchy Speci c nodes may be responsible for data collection and other nodes may be responsible for correlation and initiating responses Further, intrusion detection data and alerts may only be shared through the hierarchy, thus minimizing the overhead traf c generated by the IDS scheme We will now discuss each of these two approaches in more detail 5421 Peer-to-Peer IDS Architecture In the peer-to-peer approach every node tends to act independently of other nodes Each node has its own local detectors that are used for detecting attacks To improve the detection accuracy at each node, nodes share information with other nodes in the network on what they are observing Each node monitors for suspicious activities by monitoring traf c terminating on that node (eg port scans) Each node also tends to monitor its neighbors either through promiscuous monitoring or by inspecting traf c destined for other nodes that is routed through it When malicious activity is detected by the detectors on a node, its detectors generate alerts that are sent to all other nodes in the network The other nodes can then use that information to con rm detection of attacks within those nodes and increase the con dence of their own detection Based on the local intrusion detection and alerts from others, nodes can also determine appropriate responses to the attacks Examples of such responses include not routing traf c through a malicious node and not forwarding malicious traf c generated by a malicious node In order to reduce the potential harm from malicious nodes wrongly accusing well-behaved nodes of launching attacks, each node should trust local information much more than alerts received from other nodes In the peer-to-peer architecture, in addition to alerts, nodes may also share with other nodes local data about observed events This may help the IDS modules in other nodes detect attacks that could not have been discovered by them based exclusively on their local data For example, for detecting malicious port scanning activities it is usually bene cial to collect statistics across multiple nodes If the raw data needed by the intrusion detection algorithms is shared with every node in the network then the detector running on each node will have the ability to perform much more accurate detection of stealthy attacks (attacks that do not exhibit suf cient suspicious activity on a single node) However, the amount of IDS data that can be shared across all nodes needs to be limited because otherwise the level of overhead in terms of bandwidth used and delay incurred could be very large Figure 55 illustrates the peer-to-peer IDS architecture at a high level Here each circle represents a node executing the IDS functions As shown in the gure, different nodes are able to exchange data with each other The main advantage of the peer-to-peer approach is that the IDS architecture is fully distributed A fully distributed approach makes the IDS architecture much more resilient Every node acts independently of other nodes and does not rely on any other node for detecting attacks In a MANET environment nodes move around and lose connectivity to other nodes, and networks join and split All this makes reliance on other nodes and any centralized components problematic The other key advantage of the peer-to-peer approach and its distributed nature is its tolerance to attacks against the IDS architecture from malicious nodes A malicious IDS node can only have a limited impact on the overall intrusion detection process because each node trusts mainly its own evidence The data received from other nodes.

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